Adjacent planes rendered in very different colors?
I think this is due only to the HDRI lighting. I tried with a different, more uniform world lighting and all planes are shaded in a more "uniform" way.



I'm not an expert, but even if the two plane's normal are close, or identical, the planes position is not the same (and cannot be the same) respect to every HDRI pixel lighting the scene.

Since this is not a uniform light color, and because a single flat plane can "reflect" just one shade, this is to be taken into account. Probably a real object like that would appear the same. 

As said, normals smoothing can't help you here, because all square meshes are separate: if you can join them to appear as a single plane (although with those separating "cylinders" all above them) maybe, but I'm not sure it would give desired results anyway.

Btw, you have some plane with inverted normals, here and there...